In OFDM communication systems, users are allocated a specific number of sub-carriers for a predetermined amount of time. These are referred to as physical Resource Blocks and have both a time and frequency dimension. In contrast to packet-oriented networks, OFDM communication systems do not employ a pre-amble to facilitate carrier offset estimates, channel estimation, timing synchronization, etc. Instead, special Reference Signals are embedded in the physical Resource Blocks. A specified Reference Signal is assigned to each cell within an OFDM network and acts as a cell-specific identifier. These Reference Signals are used by User Equipment (UE) to determine the channel impulse response from each transmitting antenna.
In addition to the above-referenced cell-specific Reference Signals, UE-specific Reference Signal has been proposed by the third generation partnership project (3GPP) standards organization. These proposed UE-specific Reference Signals are transmitted only in scheduled Resource Blocks. Selected Reference Signals can be associated with different spatial multiplexing channels, or layers, within Multiple Input/Multiple Output (MIMO) OFDM communication systems. Different layers can target the same or different user equipment in the OFDM communication system.
FIG. 1 depicts a simplified OFDM communication system 10 including a base station/eNodeB 12 communicating to user equipment 14 via a MIMO communication channel 16. FIG. 2 depicts selected elements of the base station 12, where as FIG. 3 depicts selected elements of the UE 14. As seen in FIG. 2, a demodulation Reference Signal is generated by a Reference Signal generator 16 and pre-coded by a pre-coder 18 according to the number of layers, or spatial multiplexing channels, between the base station 12 and the UE 14. A time frequency mapper acts to map the pre-coded Reference Signals into Resource Blocks for transmission to UE 14. As the Reference Signals and other data are pre-coded with the same pre-coder matrix, the base station 12 does not have to inform the UE 14 which pre-coder matrix was used.
As seen in FIG. 3, at the UE 14, a time-frequency de-mapper 22 de-maps the Reference Signals from the transmitted Resource Blocks and a channel estimator 24 then estimates the effective channel, that is the product of the channel itself and the pre-coder matrix for demodulation of the data by a data demodulator 26. Different numbers of layers lead to different pre-coder matrix sizes and hence a different number of antenna ports, there being one antenna port per layer.
The mathematical derivation of a pre-coded Reference Signal design will now be described.
Assume that the maximum number of transmit antennas is 8 and let:
r denote the number of layers (or transmission rank);
d(fn, tn) denote the data vector of length r, at the subcarrier fn, OFDM symbol tn;
y(fn, tn) denote the received data vector of length up to 8, at the subcarrier fn, OFDM symbol tn (received signal at receive antennas);
H(fn, tn) denote the channel matrix of size up to 8×8, at the subcarrier fn, OFDM symbol tn; and
W denote the precoder matrix of size 8×r.
Then the received signal, transmitted data and channel relates to each other (in the absence of noise) as follows:
                    y                  8          ×          1                    ⁡              (                              f            n                    ,                      t            n                          )              =                            H                      8            ×            8                          ⁡                  (                                    f              n                        ,                          t              n                                )                    ×              W                  8          ×          r                    ×                        d                      r            ×            1                          ⁡                  (                                    f              n                        ,                          t              n                                )                                        y                  8          ×          1                    ⁡              (                              f            n                    ,                      t            n                          )              =                            A                      8            ×            r                          ⁡                  (                                    f              n                        ,                          t              n                                )                    ×                        d                      r            ×            1                          ⁡                  (                                    f              n                        ,                          t              n                                )                    
In order to recover the data d(fn, tn) from the received signal y(fn, tn), the UE needs to estimate the channel matrix A(fn, tn).
Let P(fn, tn) denote a demodulation reference signal (DRS) vector of length r at the sub-carrier fn, OFDM symbol tn, then we have
            z              8        ×        1              ⁡          (                        f          n                ,                  t          n                    )        =                    A                  8          ×          r                    ⁡              (                              f            n                    ,                      t            n                          )              ×                  p                  r          ×          1                    ⁡              (                              f            n                    ,                      t            n                          )            
Consider one element of z(fn, tn), say z1(fn, tn), i.e. the signal at the first receive antenna. Then we have:z1(fn,tn)=A11(fn,tn)p1(fn,tn)+A12(fn,tn)p2(fn,tn)+ . . . +A1r(fn,tn)Pr(fn,tn)
To solve for the unknowns A11(fn, tn), A12(fn, tn), . . . , A1r(fn, tn) we need at least r equations.
A solution is to assume the channel is the same for a number of sub-carriers, f1, f2, . . . , fr and a number of OFDM symbol t1, t2, . . . , tr and denote just by A.
Consider the system of linear equations:
                    z        1            ⁡              (                              f            1                    ,                      t            1                          )              =                            A          11                ⁢                              p            1                    ⁡                      (                                          f                1                            ,                              t                1                                      )                              +                        A          12                ⁢                              p            2                    ⁡                      (                                          f                1                            ,                              t                1                                      )                              +      …      +                        A                      1            ⁢                                                  ⁢            r                          ⁢                              p            r                    ⁡                      (                                          f                1                            ,                              t                1                                      )                                                  z        1            ⁡              (                              f            2                    ,                      t            2                          )              =                            A          11                ⁢                              p            1                    ⁡                      (                                          f                2                            ,                              t                2                                      )                              +                        A          12                ⁢                              p            2                    ⁡                      (                                          f                2                            ,                              t                2                                      )                              +      …      +                        A                      1            ⁢                                                  ⁢            r                          ⁢                              p            r                    ⁡                      (                                          f                2                            ,                              t                2                                      )                                …                    z        1            ⁡              (                              f            r                    ,                      t            r                          )              =                            A          11                ⁢                              p            1                    ⁡                      (                                          f                r                            ,                              t                r                                      )                              +                        A          12                ⁢                              p            2                    ⁡                      (                                          f                r                            ,                              t                r                                      )                              +      …      +                        A                      1            ⁢                                                  ⁢            r                          ⁢                              p            r                    ⁡                      (                                          f                r                            ,                              t                r                                      )                              
This system of equations can also be written as:
      [                                                      z              1                        ⁡                          (                                                f                  1                                ,                                  t                  1                                            )                                                                                      z              1                        ⁡                          (                                                f                  2                                ,                                  t                  2                                            )                                                            ⋮                                                                z              1                        ⁡                          (                                                f                  r                                ,                                  t                  r                                            )                                            ]    =            [                                                                  p                1                            ⁡                              (                                                      f                    1                                    ,                                      t                    1                                                  )                                                                                        p                2                            ⁡                              (                                                      f                    1                                    ,                                      t                    1                                                  )                                                          …                                                              p                r                            ⁡                              (                                                      f                    1                                    ,                                      t                    1                                                  )                                                                                                        p                1                            ⁡                              (                                                      f                    2                                    ,                                      t                    2                                                  )                                                                                        p                2                            ⁡                              (                                                      f                    2                                    ,                                      t                    2                                                  )                                                          …                                                              p                r                            ⁡                              (                                                      f                    2                                    ,                                      t                    2                                                  )                                                                          ⋮                                ⋮                                ⋮                                ⋮                                                                              p                1                            ⁡                              (                                                      f                    r                                    ,                                      t                    r                                                  )                                                                                        p                2                            ⁡                              (                                                      f                    r                                    ,                                      t                    r                                                  )                                                          …                                                              p                r                            ⁡                              (                                                      f                    r                                    ,                                      t                    r                                                  )                                                        ]        ×                  [                                                            A                11                                                                                        A                12                                                                        ⋮                                                                          A                                  1                  ⁢                  r                                                                    ]            .      
By doing similarly for other receive antennas, then we have
            [                                                                  z                m                            ⁡                              (                                                      f                    1                                    ,                                      t                    1                                                  )                                                                                                        z                m                            ⁡                              (                                                      f                    2                                    ,                                      t                    2                                                  )                                                                          ⋮                                                                              z                m                            ⁡                              (                                                      f                    r                                    ,                                      t                    r                                                  )                                                        ]        =                            [                                                                                          p                    1                                    ⁡                                      (                                                                  f                        1                                            ,                                              t                        1                                                              )                                                                                                                    p                    2                                    ⁡                                      (                                                                  f                        1                                            ,                                              t                        1                                                              )                                                                              …                                                                                  p                    r                                    ⁡                                      (                                                                  f                        1                                            ,                                              t                        1                                                              )                                                                                                                                            p                    1                                    ⁡                                      (                                                                  f                        2                                            ,                                              t                        2                                                              )                                                                                                                    p                    2                                    ⁡                                      (                                                                  f                        2                                            ,                                              t                        2                                                              )                                                                              …                                                                                  p                    r                                    ⁡                                      (                                                                  f                        2                                            ,                                              t                        2                                                              )                                                                                                      ⋮                                            ⋮                                            ⋮                                            ⋮                                                                                                          p                    1                                    ⁡                                      (                                                                  f                        r                                            ,                                              t                        r                                                              )                                                                                                                    p                    2                                    ⁡                                      (                                                                  f                        r                                            ,                                              t                        r                                                              )                                                                              …                                                                                  p                    r                                    ⁡                                      (                                                                  f                        r                                            ,                                              t                        r                                                              )                                                                                ]                          ︸          P                    ×              [                                                            A                                  m                  ⁢                                                                          ⁢                  1                                                                                                        A                                  m                  ⁢                                                                          ⁢                  2                                                                                        ⋮                                                                          A                mr                                                    ]              ,          ⁢      m    =    1    ,  …  ⁢          ,  8
Given the matrix P of DRS sequences and zm(fn, tn), m=1, . . . , 8, n=1, . . . , r, we can derive A.
It is required that DRSs on different layers are mutually orthogonal. This means P needs to satisfy:PHP=αI 
The natural and also best solution to this requirement is to designP=λI,α=|λ|2,i.e.
  P  =      [                                                      p              1                        ⁡                          (                                                f                  1                                ,                                  t                  1                                            )                                                0                          …                          0                                      0                                                    p              2                        ⁡                          (                                                f                  2                                ,                                  t                  2                                            )                                                …                          0                                      ⋮                          ⋮                          ⋱                          ⋮                                      0                          0                          …                                                    p              r                        ⁡                          (                                                f                  r                                ,                                  t                  r                                            )                                            ]  Note: it is not necessary that t1≠t2≠ . . . ≠tr.
This solution is the generalization of the UE specific reference signal in LTE Release-8. In that particular case, W is just a column vector and P is just a scalar.
This solution is the generalization of the cell specific reference signals for 2 transmit antennas in LTE Release-8. In that particular case, W=I and t1=t2, p1(f1, t1)=R0, p2(f2, t2)=R1.
This solution can also be the generalization of the cell specific reference signals for 4 transmit antennas in LTE Release-8. In that particular case, W=I, t1=t2, t3=t4, p1(f1, t1)=R0, p2(f2, t2)=R1, p3(f3, t3)=R2 and p4(f4, t4)=R3.
It is required that the design principle is an extension of the concept of the LTE Release-8 UE-specific reference signal (used for beam forming) to multiple layers, the reference signal sequence, i.e. value of pn(fn, tn), should be generated in the same way as that of the LTE Release-8 UE specific reference signals.
There exists a need to allocate elements of P into each Resource Block for different number of layers r.